Tentukan penyelesaian dari setiap persamaan logaritma berikut. c. 4log (2x+3)=2log (x+1)

Pertanyaan

Tentukan penyelesaian dari setiap persamaan logaritma berikut.

c. log presuperscript 4 space open parentheses 2 x plus 3 close parentheses equals log presuperscript 2 space open parentheses x plus 1 close parentheses

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Jawaban

penyelesaian dari log presuperscript 4 space open parentheses 2 x plus 3 close parentheses equals log presuperscript 2 space open parentheses x plus 1 close parentheses adalah x equals negative square root of 2 atau x equals square root of 2.

Pembahasan

Ingat kembali sifat logaritma 

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b end cell equals cell fraction numerator log space b over denominator log space a end fraction end cell row cell log presuperscript a space b to the power of m end cell equals cell m log presuperscript a space b end cell row cell log presuperscript a space a end cell equals 1 end table

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 4 space open parentheses 2 x plus 3 close parentheses end cell equals cell log presuperscript 2 space open parentheses x plus 1 close parentheses end cell row cell fraction numerator log space open parentheses 2 x plus 3 close parentheses over denominator 2 space log space 2 end fraction end cell equals cell log presuperscript 2 space open parentheses x plus 1 close parentheses end cell row cell 1 half log presuperscript 2 space open parentheses 2 x plus 3 close parentheses end cell equals cell log presuperscript 2 space open parentheses x plus 1 close parentheses end cell row cell log presuperscript 2 space open parentheses 2 x plus 3 close parentheses to the power of 1 half end exponent end cell equals cell log presuperscript 2 space open parentheses x plus 1 close parentheses end cell row cell open parentheses 2 x plus 3 close parentheses to the power of 1 half end exponent end cell equals cell left parenthesis x plus 1 right parenthesis end cell row cell open parentheses 2 x plus 3 close parentheses end cell equals cell left parenthesis x plus 1 right parenthesis squared space end cell row cell left parenthesis 2 x plus 3 right parenthesis end cell equals cell x squared plus 2 x plus 1 end cell row cell x squared minus 2 end cell equals 0 row cell open parentheses x plus square root of 2 close parentheses open parentheses x minus square root of 2 close parentheses end cell equals 0 end table

Jadi, penyelesaian dari log presuperscript 4 space open parentheses 2 x plus 3 close parentheses equals log presuperscript 2 space open parentheses x plus 1 close parentheses adalah x equals negative square root of 2 atau x equals square root of 2.

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